Sistemas y Señales Biomédicos

Ingeniería Biomédica

Ph.D. Pablo Eduardo Caicedo Rodríguez

2026-01-21

Sistemas y Señales Biomedicos - SYSB

Unit Step

Continous

\[u(t) = \begin{cases} 0, & t < 0 \\ 1, & t \geq 0 \end{cases}\]

Discrete

\[u[n] = \begin{cases} 0, & n < 0 \\ 1, & n \geq 0 \end{cases}\]

Unit Ramp

Continous

\[u(t) = \begin{cases} 0, & t < 0 \\ t, & t \geq 0 \end{cases}\]

Discrete

\[u[n] = \begin{cases} 0, & n < 0 \\ n, & n \geq 0 \end{cases}\]

Sync Function

Continous

\[\text{sinc}(t) = \begin{cases} \frac{\sin(\pi t)}{\pi t}, & t \neq 0 \\ 1, & t = 0 \end{cases}\]

Discrete

\[\text{sinc}[n] = \begin{cases} \frac{\sin(\pi n)}{\pi n}, & n \neq 0 \\ 1, & n = 0 \end{cases}\]

Dirac’s Delta

Continous

\[\delta(t) = \begin{cases} +\infty, & t = 0 \\ 0, & t \neq 0 \end{cases}\]

\(\int_{-\infty}^{\infty} \delta(t) dt = 1\)

Discrete

\[\delta[n] = \begin{cases} 1, & n = 0 \\ 0, & n \neq 0 \end{cases}\]

Basic Transformations on Singular signals – Translation in time

Basic Transformations on Singular signals – Translation in amplitude

Basic Transformations on Singular signals – scailing in time

Basic Transformations on Singular signals – scailing in amplitude

Example

How can i create the following signal using only singular signals

\[x(t) = 5u(t) - 5(t-3)\]

t = np.linspace(-10,10,1000)
x = np.zeros(t.shape)

x[t>=0]=5
x[t>=3]=0

plt.figure(figsize=(16,6.75))
plt.plot(t,x)
plt.grid()
plt.xlabel("Time(s)")
plt.ylabel("Amplitude")
t = np.linspace(-10,10,1000)
x = np.zeros(t.shape)

x=5*np.heaviside(t,1)-5*np.heaviside(t-3,1)

plt.figure(figsize=(16,6.75))
plt.plot(t,x)
plt.grid()
plt.xlabel("Time(s)")
plt.ylabel("Amplitude")

Exercisae Singular Signals

How can i create the following signal using only singular signals